Question

Find k if (4^k)-(4^k-1)=48

Answer 1

Answer:

Required numeric value of k is 3.

Step-by-step explanation:

Given that 4^( k ) - 4^( k - 1 ) = 48

= > 4^( k ) - { 4^( k ) } / { 4^( 1 ) } = 48

= > 4^( k ) [ 1 - ( 1 / 4 ) ] = 48

= > 4^( k ) [ ( 4 - 1 ) / 4 ] = 48

= > 4^( k ) [ 3 / 4 ] = 48

= > 4^( k ) = 48 x 4 / 3

= > 4^( k ) = 16 x 3 x 4 / 3

= > 4^( k ) = 16 x 4

= > 4^( k ) = 4^3

When bases are same, powers are equal.

= > k = 3

Hence the required numeric value of k is 3 .